Customer Segmentation

Customer Segmentation is one of key components of any business. It helps the business in product testing, targeting a specific group and to make other such important decisions.

The data set refers to clients of a wholesale distributor. It includes the annual spending in monetary units (m.u.) on diverse product categories.

The data has been taken from Kaggle. It has the following features:

• Channel - Horeca (Hotel/Restaurant/Cafe) or Retail channel (Nominal)

• Region - Region as Lisnon, Oporto or Other (Nominal)

• Fresh - annual spending (m.u.) on fresh products (Continuous)

• Milk - annual spending (m.u.) on milk products (Continuous)

• Grocery - annual spending (m.u.)on grocery products (Continuous)

• Frozen - annual spending (m.u.)on frozen products (Continuous)

• Detergents_Paper - annual spending (m.u.) on detergents and paper products (Continuous)

• Delicassen - annual spending (m.u.)on and delicatessen products (Continuous);

In this Assignment

Step 1: Understand the dataset

Step 2: Exploratory Data Analysis

Step 3: Principal Component Analysis

Step 4: Kernel Principal Component Analysis

Step 5: K-Means Clustering with Elbow Method

Step 6: Interactive Cluster Analysis

import pandas as pd
import numpy as np
import matplotlib 
%matplotlib inline
%config InlineBackend.figure_format = 'svg'
import matplotlib.pyplot as plt
plt.style.use('ggplot')

import seaborn as sns

df = pd.read_csv('Wholesale customers data.csv')
df.head()

	Channel	Region	Fresh	Milk	Grocery	Frozen	Detergents_Paper	Delicassen
0	2	3	12669	9656	7561	214	2674	1338
1	2	3	7057	9810	9568	1762	3293	1776
2	2	3	6353	8808	7684	2405	3516	7844
3	1	3	13265	1196	4221	6404	507	1788
4	2	3	22615	5410	7198	3915	1777	5185

# Renaming the column and grouping the categorical features
df = df.rename(columns={'Delicassen': 'Delicatessen'})
df['Channel'] = df['Channel'].map({1: 'HoReCa', 2: 'Retail'})
df['Region'] = df['Region'].map({1: 'Lisbon', 2: 'Porto', 3: 'Other'})
df.head()

	Channel	Region	Fresh	Milk	Grocery	Frozen	Detergents_Paper	Delicatessen
0	Retail	Other	12669	9656	7561	214	2674	1338
1	Retail	Other	7057	9810	9568	1762	3293	1776
2	Retail	Other	6353	8808	7684	2405	3516	7844
3	HoReCa	Other	13265	1196	4221	6404	507	1788
4	Retail	Other	22615	5410	7198	3915	1777	5185

features = df.columns.to_list()       # list of all the features

df.info()                            # data types and null values

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 440 entries, 0 to 439
Data columns (total 8 columns):
 #   Column            Non-Null Count  Dtype 
---  ------            --------------  ----- 
 0   Channel           440 non-null    object
 1   Region            440 non-null    object
 2   Fresh             440 non-null    int64 
 3   Milk              440 non-null    int64 
 4   Grocery           440 non-null    int64 
 5   Frozen            440 non-null    int64 
 6   Detergents_Paper  440 non-null    int64 
 7   Delicatessen      440 non-null    int64 
dtypes: int64(6), object(2)
memory usage: 27.6+ KB

df.describe()            # statistical information

	Fresh	Milk	Grocery	Frozen	Detergents_Paper	Delicatessen
count	440.000000	440.000000	440.000000	440.000000	440.000000	440.000000
mean	12000.297727	5796.265909	7951.277273	3071.931818	2881.493182	1524.870455
std	12647.328865	7380.377175	9503.162829	4854.673333	4767.854448	2820.105937
min	3.000000	55.000000	3.000000	25.000000	3.000000	3.000000
25%	3127.750000	1533.000000	2153.000000	742.250000	256.750000	408.250000
50%	8504.000000	3627.000000	4755.500000	1526.000000	816.500000	965.500000
75%	16933.750000	7190.250000	10655.750000	3554.250000	3922.000000	1820.250000
max	112151.000000	73498.000000	92780.000000	60869.000000	40827.000000	47943.000000

EDA

In this section we will see the relationship among different features and also the data distribution within each.

df.head()

	Channel	Region	Fresh	Milk	Grocery	Frozen	Detergents_Paper	Delicatessen
0	Retail	Other	12669	9656	7561	214	2674	1338
1	Retail	Other	7057	9810	9568	1762	3293	1776
2	Retail	Other	6353	8808	7684	2405	3516	7844
3	HoReCa	Other	13265	1196	4221	6404	507	1788
4	Retail	Other	22615	5410	7198	3915	1777	5185

df.Region.value_counts()

Other     316
Lisbon     77
Porto      47
Name: Region, dtype: int64

df.Channel.value_counts()

HoReCa    298
Retail    142
Name: Channel, dtype: int64

## Visualizing the feature via histplot 

fig, axes = plt.subplots(2, 4, figsize=(9,6))

for feature, ax in zip(features, axes.ravel()):
    if (feature=='Channel') | (feature=='Region'):
        df[feature].value_counts().plot.bar(ax=ax, color='green')
    else:
        ax.hist(df[feature], bins=100, color='green')
    ax.set_title(feature)
plt.tight_layout()   

# To visualize the relationship between 2 features
pplot = sns.pairplot(df, vars=features[2:])
pplot.fig.set_size_inches(7,7)

features = ['Fresh','Milk','Grocery','Frozen','Detergents_Paper','Delicatessen']

data = df[features].to_numpy()
data.shape

(440, 6)

Scaling the data

from sklearn.preprocessing import StandardScaler
from sklearn.decomposition import PCA

scaler = StandardScaler()
data = scaler.fit_transform(data)
data[:, 0].std()

1.0

PCA

Reducing the dimensionality of the data using Principal Component Analysis. In this section we will see how the performance varies from PCA to Kernel PCA and also among the different kernel types: Poly, Cosine and RBF

pca = PCA(n_components=2)
res_pca = pca.fit_transform(data)

plt.scatter(res_pca[:, 0], res_pca[:, 1], s=3, alpha=0.3)

<matplotlib.collections.PathCollection at 0x1a67dd48940>

def scatter(pca):
    fig, axes = plt.subplots(2, 3, figsize=(7, 5))

    for feature, ax in zip(features, axes.ravel()):
        cmap = 'viridis'
        sizes = 20+5*data[:, features.index(feature)]
        cols = df[feature]
        ax.scatter(pca[:, 0], pca[:, 1], s=sizes, c=cols, cmap=cmap)
        ax.set_title(feature)
    plt.tight_layout()

scatter(res_pca)

def cat_scatter(pca):
    fig, axes = plt.subplots(2,1, figsize=(7, 5))

    for feature, ax in zip(['Channel', 'Region'], axes.ravel()):
        cmap = 'Pastel1'
        sizes = 20
        for unique_val in df[feature].unique():
            ax.scatter(pca[df[feature]==unique_val, 0], 
                       pca[df[feature]==unique_val, 1],
                       label = unique_val)

        ax.set_title(feature)
        ax.legend()
    plt.tight_layout()

cat_scatter(res_pca)

Kernel PCA

Let's see whether Kernel PCA performs better

Poly Function

from sklearn.decomposition import KernelPCA

kpca = KernelPCA(n_components=2, kernel='poly', degree=3)
res_kpca_poly = kpca.fit_transform(data)

scatter(res_kpca_poly)

cat_scatter(res_kpca_poly)

Radial Basis Function

kpca = KernelPCA(n_components=2, kernel='rbf', gamma=0.01)
res_kpca_rbf = kpca.fit_transform(data)

scatter(res_kpca_rbf)

cat_scatter(res_kpca_rbf)

Cosine Function

kpca = KernelPCA(n_components=2, kernel='cosine')
res_kpca_cos = kpca.fit_transform(data)

scatter(res_kpca_cos)

cat_scatter(res_kpca_cos)

# Combining in a single dataframe
df['x_kpca_poly'] = res_kpca_poly[:, 0]
df['y_kpca_poly'] = res_kpca_poly[:, 1]

df['x_kpca_rbf'] = res_kpca_rbf[:, 0]
df['y_kpca_rbf'] = res_kpca_rbf[:, 1]

df['x_kpca_cos'] = res_kpca_cos[:, 0]
df['y_kpca_cos'] = res_kpca_cos[:, 1]

df.head()

	Channel	Region	Fresh	Milk	Grocery	Frozen	Detergents_Paper	Delicatessen	x_kpca_poly	y_kpca_poly	x_kpca_rbf	y_kpca_rbf	x_kpca_cos	y_kpca_cos
0	Retail	Other	12669	9656	7561	214	2674	1338	-1.250715	-1.129890	0.019291	-0.043521	0.504789	0.009622
1	Retail	Other	7057	9810	9568	1762	3293	1776	-1.246319	-1.103619	0.051053	-0.072161	0.889941	-0.262833
2	Retail	Other	6353	8808	7684	2405	3516	7844	-0.443468	-1.124730	0.085747	0.005375	0.473994	0.235687
3	HoReCa	Other	13265	1196	4221	6404	507	1788	-1.243229	-1.168208	-0.108671	0.061805	-0.618611	0.370131
4	Retail	Other	22615	5410	7198	3915	1777	5185	-0.977592	-1.156057	-0.010585	0.130396	0.068900	0.861829

K-Means Algorithm

from sklearn.cluster import KMeans

from yellowbrick.cluster import KElbowVisualizer

features = ['Fresh','Milk','Grocery','Frozen','Detergents_Paper','Delicatessen']

res_kpca = df[['x_kpca_rbf', 'y_kpca_rbf']].to_numpy()

clusterer = KMeans(n_clusters=5)
clusters = clusterer.fit_predict(res_kpca)

markers = list('*hH+xXDd|.,ov^<>12348spP')

for cluster in np.unique(clusters):
    cluster_data = res_kpca[clusters==cluster]
    plt.scatter(cluster_data[:, 0], cluster_data[:, 1], alpha=0.7, marker=markers[cluster])

fig, axes = plt.subplots(2, 3, figsize=(16, 8))

for feature, ax in zip(features, axes.ravel()):
    cols = 'viridis'
    for cluster in np.unique(clusters):
        sizes = 20+3*data[:, features.index(feature)][clusters==cluster]
        cluster_data = res_kpca[clusters==cluster]
        ax.scatter(cluster_data[:, 0], cluster_data[:, 1], s=sizes, alpha=0.6, cmap=cols, marker=markers[cluster], label=f'Cluster {cluster}')
    ax.set_title(feature)
plt.tight_layout()

Elbow Method

We will verify our assumption of k=5 using the elbow method

df['cluster_kpca_cos'] = clusters

clusterer = KMeans()
visualizer = KElbowVisualizer(clusterer, k=(2, 12), metric='distortion')

visualizer.fit(res_kpca)        
visualizer.show()

<AxesSubplot:title={'center':'Distortion Score Elbow for KMeans Clustering'}, xlabel='k', ylabel='distortion score'>

df.head()

	Channel	Region	Fresh	Milk	Grocery	Frozen	Detergents_Paper	Delicatessen	x_kpca_poly	y_kpca_poly	x_kpca_rbf	y_kpca_rbf	x_kpca_cos	y_kpca_cos	cluster_kpca_cos
0	Retail	Other	12669	9656	7561	214	2674	1338	-1.250715	-1.129890	0.019291	-0.043521	0.504789	0.009622	1
1	Retail	Other	7057	9810	9568	1762	3293	1776	-1.246319	-1.103619	0.051053	-0.072161	0.889941	-0.262833	0
2	Retail	Other	6353	8808	7684	2405	3516	7844	-0.443468	-1.124730	0.085747	0.005375	0.473994	0.235687	0
3	HoReCa	Other	13265	1196	4221	6404	507	1788	-1.243229	-1.168208	-0.108671	0.061805	-0.618611	0.370131	4
4	Retail	Other	22615	5410	7198	3915	1777	5185	-0.977592	-1.156057	-0.010585	0.130396	0.068900	0.861829	4

df.groupby(['cluster_kpca_cos', 'Channel', 'Region'])[features].mean()

			Fresh	Milk	Grocery	Frozen	Detergents_Paper	Delicatessen
cluster_kpca_cos	Channel	Region
0	HoReCa	Lisbon	6138.400000	13508.400000	11089.600000	3497.800000	3103.000000	2299.600000
		Other	5945.200000	12733.600000	11024.200000	2671.600000	3924.400000	2532.600000
	Retail	Lisbon	3114.600000	9248.100000	17184.000000	1266.600000	7288.100000	1817.900000
		Other	5814.241379	9139.431034	15181.724138	1341.120690	6627.327586	1543.413793
		Porto	3399.363636	10993.636364	16652.636364	1041.636364	8338.363636	1022.636364
1	HoReCa	Lisbon	6770.918919	2736.351351	2908.675676	2396.864865	891.945946	666.594595
		Other	6472.772727	2633.863636	3283.734848	1702.863636	729.962121	932.598485
		Porto	7882.444444	1661.055556	3979.888889	2457.000000	503.777778	818.000000
	Retail	Lisbon	2665.500000	3632.000000	5677.000000	4279.000000	3052.000000	740.000000
		Other	10496.920000	5472.760000	7584.280000	1217.480000	2865.120000	1075.920000
		Porto	9721.000000	3974.750000	7136.250000	907.500000	3280.000000	956.750000
2	HoReCa	Lisbon	46851.250000	4824.500000	4534.000000	8347.000000	822.000000	2317.000000
		Other	48824.230769	10350.923077	10100.153846	14983.692308	1340.384615	7827.153846
		Porto	32717.000000	16784.000000	13626.000000	60869.000000	1272.000000	5609.000000
3	Retail	Lisbon	6317.250000	20614.250000	33618.500000	3802.500000	16386.750000	2586.500000
		Other	15041.785714	31030.357143	38100.642857	2181.428571	17792.928571	4007.642857
		Porto	9162.000000	15025.500000	42471.500000	629.500000	25255.000000	1420.000000
4	HoReCa	Lisbon	22508.615385	3096.692308	4333.615385	3457.769231	328.923077	1938.615385
		Other	23105.278689	3112.344262	3282.377049	5552.163934	534.229508	1358.016393
		Porto	16846.000000	1981.777778	4201.111111	6196.222222	352.888889	1181.333333
	Retail	Lisbon	15927.000000	5955.000000	7413.500000	5040.000000	1761.500000	1845.000000
		Other	27759.250000	6459.375000	8949.250000	2515.500000	2413.250000	2403.625000
		Porto	21952.500000	3872.500000	6766.500000	6462.000000	2221.500000	2812.500000

df.groupby(['cluster_kpca_cos']).count()

	Channel	Region	Fresh	Milk	Grocery	Frozen	Detergents_Paper	Delicatessen	x_kpca_poly	y_kpca_poly	x_kpca_rbf	y_kpca_rbf	x_kpca_cos	y_kpca_cos
cluster_kpca_cos
0	89	89	89	89	89	89	89	89	89	89	89	89	89	89
1	218	218	218	218	218	218	218	218	218	218	218	218	218	218
2	18	18	18	18	18	18	18	18	18	18	18	18	18	18
3	20	20	20	20	20	20	20	20	20	20	20	20	20	20
4	95	95	95	95	95	95	95	95	95	95	95	95	95	95

clusters = df.cluster_kpca_cos

df_normalized = df.copy(deep=True)
df_normalized.loc[:, features] = data

df.head()

	Channel	Region	Fresh	Milk	Grocery	Frozen	Detergents_Paper	Delicatessen	x_kpca_poly	y_kpca_poly	x_kpca_rbf	y_kpca_rbf	x_kpca_cos	y_kpca_cos	cluster_kpca_cos
0	Retail	Other	12669	9656	7561	214	2674	1338	-1.250715	-1.129890	0.019291	-0.043521	0.504789	0.009622	1
1	Retail	Other	7057	9810	9568	1762	3293	1776	-1.246319	-1.103619	0.051053	-0.072161	0.889941	-0.262833	0
2	Retail	Other	6353	8808	7684	2405	3516	7844	-0.443468	-1.124730	0.085747	0.005375	0.473994	0.235687	0
3	HoReCa	Other	13265	1196	4221	6404	507	1788	-1.243229	-1.168208	-0.108671	0.061805	-0.618611	0.370131	4
4	Retail	Other	22615	5410	7198	3915	1777	5185	-0.977592	-1.156057	-0.010585	0.130396	0.068900	0.861829	4

biggest_cluster = df.groupby(['cluster_kpca_cos']).count().max().max()

Interactive Cluster Analaysis

import plotly.graph_objects as go

fig = go.Figure()

for cluster in np.unique(clusters):
    
    radii = df_normalized.loc[df_normalized.cluster_kpca_cos==cluster, features].values[0].tolist()
    thetas = features
    
    actual_values = df.loc[df.cluster_kpca_cos==cluster, features].values[0].tolist()
    cluster_size = len(df[df.cluster_kpca_cos==cluster])
#     print(cluster_size)
    fig.add_trace(
        go.Scatterpolar(
            r=radii + radii[:1],
            theta=thetas + thetas[:1],
            mode='lines',
            name=f'Cluster {cluster}',
            text = [f'Mean value: {x}' for x in actual_values + actual_values[:1]],
            line=dict(width=3),
            opacity=np.max([cluster_size/biggest_cluster, 0.6])
        )
    )

fig.update_layout(
    title='Cluster Analysis',
    showlegend=True,
    template='plotly_dark',
    width=800,
    autosize=False
)

fig.show()

Conclusions:

We see that the k value of 5 yeilded the optimal solution and was also verified the elbow method. The 5 different clusters of customers with different preferences. We see that customers of cluster 0 behaves identically with customers of cluster 1. The business can focus on the customers of cluster 0 to increase their volume and expand the business.

Next Steps:

We can try other clustering algorithms like DBScan and Hierarchical clustering and compare the results.

Data Scource: https://www.kaggle.com/sahistapatel96/wholesale-customer-datacsv